Introduction to multiple signal classifier (music)

INTRODUCTION TO MUSIC
Contents
Introduction
The Music Algorithm
Adaptive Beamforming using MUSIC Pseudo-
Spectrum
Ppt & Simulation By Milkessa Negeri JNTUH,India

Introduction
 MUSIC stands for MUltiple SIgnal
Classification.
 Estimates set of constant parameters [from
measurements] upon which the received signals
depend.
 Thus, MUSIC is an algorithm used for frequency
estimation ,i.e
 It estimates the frequency content of a signal
or autocorrelation matrix using an Eigen
space method.

Cont….
Q:What is this Eigen space method ?
A:
Eigen space method assumes that a signal
x(n), consists of p complex exponentials in the
presence of Gaussian white noise.
MUSIC is high resolution algorithm.
Given an MxM autocorrelation matrix,𝑅 𝑥,

Cont…
If the eigenvalues are sorted in decreasing order,
the eigenvectors correspond to the p largest
eigenvalues,
The remaining M-p eigenvectors span the
orthogonal space, where there is only noise.
In other words;
Suppose you have a signal which is composed of a
sum of sinusoids (say r) plus some noise (w(n)),
that has to be strictly independent from the
signal. You have M samples of this signal, i. e, n =
0,1,2,…M-1.

1.2 Adaptive Beamforming using MUSIC
Pseudo-Spectrum
It’s obvious that The filtering operation in
adaptive filtering is performed primarily in
time domain.
In beamforming:-the filtering operation is
done in spatial domain.
It distinguishes between the spatial properties
of signal and noise.
The system used to do the beamforming
operation is called the beamformer.

Cont…
The term beamformer drived from the fact that
early antennas were designed to form pencil
beams
So as to receive source signals radiating from a
specific direction & to attenuate signals
originating from other direction that were of no
interest.
Beamforming applies to the radiation (i.e.
transmission ) as well as the reception of energy.


Cont…
Adaptive beamforming is used for enhancing a
desired signal while suppressing noise and
interference at the output of an array of sensors.
Figure 2 depicts the structure of an adaptive
beamformer.
In applications where signal always present but
its strength is unknown, application of linear
constraints to the weight vector permits
extensive control of the adaptive behavior of the
beamformer.

Cont…
Estimation of Direction of Arrival (DOA) is a vital task
in many practical applications such as smart
antennas, high-resolution radar, underwater
acoustics, noise reduction, to mention a few.
DOA estimation survives as a front end to beam
forming algorithms.
Beam forming uses an array of antennas/sensors to
transmit/receive signals to/from a specified spatial
direction in the presence of interference and noise.
Interference signals are considered as signals that
are correlated with the desired signals.

Cont…
Noise signals (a.k.a. distractors) are considered as
not correlated with the desired signals, and can be
either considered directional or ambient sources.
Conventional beamformers are based on the
delay-and-sum approach as well as on methods
that use various weight vectors for sidelobe
control.
For these beam formers the weight vectors can be
pre-determined independently of the incoming
data. As shown in Figure 1, signal y(t) can be
expressed as:

Figure 1: Conventional beamformers can use an
array of sensors to estimate DOA

Cont….
The sensor outputs(see fig. below), assumed to
be in baseband form, are individually weighted
and then summed to produce the overall
beamformer output.
The beamformer has to satisfy two requirements:
The steering capability, whereby the
target(source) signal is always protected
Cancellation of interference, so that the output
signal-to-noise ratio is maximized.

Figure 2: An adaptive beamformer enhances a desired
signal while suppressing noise and interference at the
output of an array of sensors

Cont….
Where d is the distance b/n adjacent sensors of
the array .
Ø denote the actual angle of incidence of a plane
wave .
𝜃 =
2𝜋𝑑𝑠𝑖𝑛 ∅
λ θ=
𝜋/2
−𝜋/2

Cont…
One of the more effective approaches to adaptive
control of the beamformer is the Multiple Signal
Classification (MUSIC) algorithm that uses the
eigenvectors decomposition and eigenvalues of
the covariance matrix of the antenna array for
estimating directions-of-arrival of sources based
on the properties of the signal and noise
subspaces.
A viable alternative to the MUSIC algorithm is an
approach called ESPIRIT (Estimation of Signal
Parameters via Rotational Invariance Technique).

Cont…
ESPIRIT is based on the rotational invariance property
of the signal space to make a direct estimation of the
DOA and obtain the angles of arrival without the
calculation of a pseudo-spectrum on the extent of
space.
ESPIRIT is similar to MUSIC algorithm yet with various
modifications.
The simplicity of its implementation (although at the
cost of spatial resolution degradation) is considered
as an approach of choice in some applications.
Also, ESPRIT is less sensitive to uncorrelated noise
than MUSIC.

Cont…
Figure 3 below illustrates an example comparison
between these two approaches.
While MUSIC shows better spatial resolution than
ESPIRIT, it is important to note the comparison is a
function of data; thus graphs will look differently
for each case under consideration.

Figure 3: An example comparison
between DOA generated using MUSIC
versus ESPIRIT

Simulation results
• Pmusic with no sampling specified

Specifying Sampling Frequency and Subspace Dimensions

Entering a Signal Data Matrix Generated from corrmtx

Using Windowing to Create the Effect of a Signal Data Matrix

REFERENCES
[1]
http://msol.people.uic.edu/ECE531/papers/Multipl
e%20Emitter%20Location%20and%20Signal%20Para
meter%20Estimation.pdf
[2]
https://en.wikipedia.org/wiki/MUSIC_(algorithm)
[3] https://www.vocal.com/beamforming/adaptive-
beamforming-using-music-pseudo-spectrum/

Introduction to multiple signal classifier (music)

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